wccusd grade 6 math benchmark 2 study guide · 2017-01-15 · wccusd grade 6 math benchmark 2 study...

WCCUSD Grade 6 Math Benchmark 2 Study Guide

of 7 MCC@WCCUSD (WCCUSD) 01/12/17

1

6.RP.1

2 Using ratio tables to solve problems

6.RP.3

1´ You try: A pet store has three dogs, five cats and seven rabbits in their front window. Find and write two part-to-part ratios for the story. Include a visual model (pictures, letters, etc.) to help you understand the question.

2´ You try: The ratio of students at a school is 3

boys for every 4 girls. If there are 52 girls, how many boys are at the school?

i 9

Use the picture to choose a pair of ratios that show a part to whole relationship.

!

Understanding ratio relationships. Choose the answer that shows two part-to-whole ratios that describe the group of shapes below.

i 9

i 9

3:4, 2:7

5:9, 7:9 !

A. B.

C. D.

The correct answer is C. The first ratio represents 3 triangles for every 9 shapes. The second ratio represents 4 squares for every 9 shapes. Both of these ratios are part-to-whole ratios.

**You can find equivalent ratios by entering what you know into a table, and multiplying or dividing the ratio by an equivalent form of one.

During a trip to Mexico, Kathleen exchanges 100 dollars and receives 2,000 pesos. After her trip, she has 400 pesos left. When she exchanges her pesos for dollars, how many will dollars will she receive?

Part% 14% 48%Whole% 25% 100%%%%%%

Pesos% 2,000% 400%Dollars% 100% ?%

%%

%Set$up$a$table$$with$$all$the$information$you$have.$

Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%

Divide$your$ratio$to$find$the$answer.$

Part% 14% 48%Whole% 25% 100%%%%%%

Pesos% 2,000% 400%Dollars% 100% ?%

%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


Kathleen will receive 20 dollars.



3 Finding unit rates.

.

3´ You try: Janice drove 5,700 miles in one

year. At that rate, how many miles did she drive each month? Find the unit rate by using a table.

6.RP.2

Bernard types 120 words in 3 minutes. At this rate, how many words can he type in 1 minute?

120 40 40 40

1203

= 401

÷3

÷3

**Use the information you have to set up two equivalent ratios. The first ratio has a 3 in the denominator. To find the unit rate, use division to change the denominator into a 1.

120 40 40 40

1203

=1

÷3

÷3

Divide.

Solve using equivalent ratios.

Solve using a table.

Part% 14% 48%Whole% 25% 100%%%%%%Words% 120% ?%Minutes% 3% 1%% %

%%

%%

%%

%%

%%

%

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%%

%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%

%Put$all$the$information$into$a$table.$$Divide$to$find$the$answer.$

Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


−125 %%150 −150

0

↓%

0.56

Find the unit rate by using equivalent ratios.



4 Solve using division The ratio described in the story is . This can also be seen as the division problem 14 ÷ 25 .

6.RP.3c

4´ You try: Mika rented 20 movies. 7 of the movies were comedies. What percent of the movies Mika rented were comedies?

Solving Percent Problems with Equivalent Ratios

Melanie answered 14 questions correctly on a 25 questions test. What percent of the questions did she answer correctly?

**14 out of 25 can be written as the ratio

1425

= ?100

%%%%%

1425

= 56100

%%%%%%%%%% Pesos% 2,000% 400%

Dollars% 100% ?%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


%%

%%

Multiply to find your answer.

Write two equivalent ratios, and put a 100 in the denominator of the second ratio.

So, Melanie answered 56% of the questions correctly.

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%%

%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


−125 %%150 −150

0

↓%

0.56

Divide 14 by 25.

Turn the decimal quotient into a percent.

Melanie answered 56% of the problems correctly.

Solve with equivalent ratios:

Solve using division.

Student Elevation Marsha

Jan Cindy

%%

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%

%%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%

Put all the information into a table. Divide to find the answer.

Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%

Divide&your&ratio&to&find&the&answer.&

%%150 −150

0

↓%

0.56

0



5 Integers

6.NS.6c

5´ You try: Marsha, Jan, and Cindy are scuba diving at the ocean. The number line provided shows the elevation, in feet, of each girl above and below sea level. .

Bob, Sherman, and Rocky live in three different towns. The students and the elevation of each town are included in the table below:

Student Elevation Bob −2 feet

Sherman 4 feet Rocky −3½ feet

%%

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%

%%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


−125 %%150 −150

0

↓%

0.56 Place a dot on the number line for each elevation, and then correctly label each dot B, S, or R.



%%

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%

%%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


%%150 −150

0

↓%

0.56

0

I notice there are short lines and long lines on the number line. The long lines must represent whole numbers, and the short lines must represent each half.

For Sherman, I can start at zero and count up four long lines.

For Bob, I can start at zero and count down two long lines.

For Rocky, I can start at zero and count down three long lines and one short line.

B

S

R


Sherman 4 feet Rocky −3½ feet %%

1425

=?100

%%%%%%%%%%%%%%%%%%%%%%%%25 14.00

%%%

1425

=56100

%%%%%%%%

%%

Pesos%2,000%400%

%%

%%

%Dollars%100%?%%


Pesos%2,000%400%Dollars%100%20%%

%%

%%


%%150 −150

0

↓%

0.56 0



%%

1425

=?100

%%%%%%%%%%%%%%%%%%%%%%%%25 14.00

%%%

1425

=56100

%%%%%%%%

%%

Pesos%2,000%400%

%%

%%

%Dollars%100%?%%


Pesos%2,000%400%Dollars%100%20%%

%%

%%


%%150 −150

0

↓%

0.56 0


Sherman 4 feet Rocky −3½ feet %%

1425

=?100

%%%%%%%%%%%%%%%%%%%%%%%%25 14.00

%%%

1425

=56100

%%%%%%%%

%%

Pesos%2,000%400%

%%

%%

%Dollars%100%?%%


Pesos%2,000%400%Dollars%100%20%%

%%

%%


%%150 −150

0

↓%

0.56 0

1. Use the number line to fill in the table with each girl’s elevation.



%%

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%

%%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


%%150 −150

0

↓%

0.56

0

M

J

C


Jan Cindy

%%

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%

%%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


%%150 −150

0

↓%

0.56

0

2. Write a sentence for each girl that describes what she could be doing at her elevation.

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________



6 Graphing on the coordinate plane

6´ You try: Point E is located at (4, 2).

End of Study Guide

Point A, located at (−2, −5), has been reflected across the x-axis. This “reflection” has been labeled as Point B.

1. What are the coordinates of Point B? 2. What is the distance between Point A and Point B?

1. When a point is reflected across the x-axis, the numbers stay the same, but the sign of the y-coordinate changes its sign. Therefore, the coordinates of Point B are (−2, 5). 2. Point B (−2, 5) is 5 units above the x-axis, and Point A (−2,−5) is 5 units below the x-axis. Because both points have the same x-coordinate (−2), a straight, vertical line can be drawn between them. The vertical distance between Point A and Point B is 10 units.

WCCUSD Grade 6 Benchmark 2 Study Guide

Page 5 of 14 MCC@WCCUSD (WCCUSD) 12/18/15

7 Point A located at (−2, −5), has been reflected across the x-axis. . Please plot the new point B and state its coordinates What is the distance between the two points? Please justify your answer.

Solution: Reflection across the x axis When you reflect a point across the x-axis, the x-coordinate stays the same but the y-coordinate keeps the same number but changes its sign. (Ex. (−2, − 5) becomes (−2, 5) when reflected. The distance between (−2, −5) and (−2, 5) is 10 units in a straight line crossing the x-axis at point (−2, 0). Point (−2, 5) is 5 units vertically ascending into quadrant II from the x-axis point of (−2, 0) and point (−2, −5) is 5 units vertically descending into quadrant III from point (−2, 0). Now reflect point A across both axes and call it point C. State point C’s coordinate pair. Solution: Reflection across both the x and y axes. When you reflect a point across the x and y axes, the x and y-coordinate both change their sign. (Ex. (−2, − 5) becomes (2, 5) when reflected. Point C becomes (2, 5).

6.NS.6b, 6.NS.8

7´ You try: Point E located at (4, 2) has been reflected across the y-axis. Please plot the new point F and state its coordinates. What is the distance between the two points? Please justify your answer.

Now reflect point E across both axes and call it point G. State point G’s coordinate pair.

A

B y

x E

y

x

(−2, −5)

C

1. Reflect a new point across the y-axis, and label it Point F. What are the coordinates of Point F? 2. What is the distance between Point E and Point F?





6.NS.6b, 6.NS.8



A

B y

x E

y

x

(−2, −5)

C

6.NS.8



1´ Understanding ratio relationships. You try: A pet store has three dogs, five cats and seven rabbits in their front window. Find and write two part-to-part ratios for the story.

2´ Using ratio tables to solve problems.

You try: The ratio of students at a school is 3 boys for every 4 girls. If there are 52 girls, how many boys are at the school

3´ Finding unit rates. You try: Janice drove 5,700 miles in one year. At that rate, how many miles did she drive each month?

Possible answers

(dogs : cats) 3 to 5,

(cats : rabbits) 5 : 7, 5 to 7,

(dogs : rabbits) 3 : 7, 3 to 7,

Remember that when a ratio is in fractional form, we still say “three to five”, and not “three fifths”.

Part% 14% 48%Whole% 25% 100%%%%%%

Boys% 3% ?%Girls% 4% 52%

%%%%%%% %

%%

%%

%%

%%

%% Put all the information you have into a table.

Part% 14% 48%Whole% 25% 100%%%%%%

Boys% 3% 39%Girls% 4% 52%

%%%%%%% %

%%

%%

%%

%%

%%

Multiply to find your answer.

There are 39 boys at the school.

Solve using a table.

Part% 14% 48%Whole% 25% 100%%%%%%

Miles% 5,700% 475%Months% 12% 1%

%%%%%%% %

%%

%%

%%

%%

%%


Jan Cindy

%%

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%

%%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%

Put all the information into a table. Divide to find the answer.

Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%

Divide&your&ratio&to&find&the&answer.&

%%150 −150

0

↓%

0.56

0

Solve using equivalent ratios.

Janice drove 475 miles each month.

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

5,700

12= 475

1%%

%%%%%%%

%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


−125 %%150 −150

0

↓%

0.56

Janice drove 475 miles each month.

Answers such as 3:15, or 7:15 are not correct, because those are part to whole ratios, and not part to part ratios.



4´ Solving Percent Problems You try: Mika rented 20 movies. 7 of the movies were comedies. What percent of the movies Mika rented were comedies?

5´ Integers You try: Marsha, Jan, and Cindy are scuba diving at the ocean. The number line provided shows the elevation, in feet, of each girl above and below sea level.

9´ Graphing on the coordinate plane

You try: Point E is located at (4, 2).

720

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

720

= 35100

%%%%%%%%%

%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


−125 %%150 −150

0

↓%

0.56 720

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

720

= 35100

%%%%%%%%%

%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


−125 %%150 −150

0

↓%

0.56 Solve using equivalent ratios.

of the movies Mika rented were comedies.

Solve using division.

720

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 20 7.00

%%%

720

= 35100

%%%%%%%%%

%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


−60 %%100 −100

0

↓%

0.35

, therefore of the movies Mika rented were comedies.

1. Use the number line to fill in the table with each girl’s elevation.


Jan Cindy

%%

1425

= ?100

%%%%%%%%%%%%%%%%%%% % % % % % 25 14.00

%%%

1425

= 56100

%%%%%%%%

%%

Pesos% 2,000% 400%

%%

%%

%Dollars% 100% ?%%


Pesos% 2,000% 400%Dollars% 100% 20%%

%%

%%


%%150 −150

0

↓%

0.56

0

+2 feet

−7 feet 0 feet

2. Write a sentence for each girl that describes what she could be doing at her elevation.

Accept any reasonable answer. Some examples: Marsha is sitting in the diving boat, Jan is floating at the water level, Cindy is gathering shells from the ocean floor.

1. Reflect a new point across the y-axis, and label it Point F. What are the coordinates of Point F? The coordinates are (−4, 2). 2. What is the distance between Point E and Point F? The horizontal distance between Point E and Point F is 8 units.

Part% 14% 48%Whole% 25% 100%%%%%%

Miles% 5,700% 475%Months% 12% 1%

%%%%%%% %

%%

%%

%%

%%

%%

%





6.NS.6b, 6.NS.8



A

B y

x E

y

x

(−2, −5)

C

F

wccusd grade 6 math benchmark 2 study guide · 2017-01-15 · wccusd grade 6 math benchmark 2 study...

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